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arXiv:1307.5444 · Physical Review A

Topological superfluid by blockade effects in a Rydberg-dressed Fermi gas

Bo Xiong, H. H. Jen, Daw-Wei Wang

Published Jul 30, 2014• 20 citations
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Abstract

We systematically investigate the topological superfluidity of a Rydberg-dressed Fermi gas, where the soft-core effective interaction is of finite radius ${R}_{c}$ due to the blockade effect. We calculate the quantum phase diagram within the mean-field approximation and find three distinct phases: polar $({p}_{z})$, axial $({p}_{x}+i{p}_{y})$, and axiplanar $({p}_{x}+i{\ensuremath{\beta}}_{p}{p}_{y})$ phases. The tricritical point is around ${R}_{c}{k}_{F}\ensuremath{\sim}1$, where ${k}_{F}$ is the Fermi wave vector. We further derive the Ginzburg--Landau theory to explain the phase diagram and estimate the transition temperature to be about $0.1{E}_{F}$ in the current experimental regime of $^{6}\mathrm{Li}$. Our work paves the way for future studies on exotic topological superfluids and related quantum phase transitions.

DOI
10.1103/physreva.90.013631

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We systematically investigate the topological superfluidity of a Rydberg-dressed Fermi gas, where the soft-core effective interaction is of finite radius Rc{R}_{c}Rc​ due to the blockade effect. We calculate the quantum phase diagram within the mean-field approximation and find three distinct phases: polar (pz)({p}_{z})(pz​), axial (px+ipy)({p}_{x}+i{p}_{y})(px​+ipy​), and axiplanar (px+i\ensuremathβppy)({p}_{x}+i{\ensuremath{\beta}}_{p}{p}_{y})(px​+i\ensuremathβp​py​) phases. The tricritical point is around RckF\ensuremath∼1{R}_{c}{k}_{F}\ensuremath{\sim}1Rc​kF​\ensuremath∼1, where kF{k}_{F}kF​ is the Fermi wave vector. We further derive the Ginzburg--Landau theory to explain the phase diagram and estimate the transition temperature to be about 0.1EF0.1{E}_{F}0.1EF​ in the current experimental regime of 6Li^{6}\mathrm{Li}6Li. Our work paves the way for future studies on exotic topological superfluids and related quantum phase transitions.
Interacting Fermi gas provides an ideal model system to understand unconventional pairing and intertwined orders relevant to a large class of quantum materials. Rydberg-dressed Fermi gas is a recent experimental system where the sign, strength, and range of the interaction can be controlled. The interaction in momentum space has a negative minimum at qc{q}_{c}qc​ inversely proportional to the characteristic length scale in real space, the soft-core radius rc{r}_{c}rc​. We show theoretically that single-component (spinless) Rydberg-dressed Fermi gas in two dimensions has a rich phase diagram with superfluid and density wave orders due to the interplay of the Fermi momentum pF{p}_{F}pF​, interaction range rc{r}_{c}rc​, and interaction strength u0{u}_{0}u0​. For repulsive bare interactions u0>0{u}_{0}>0u0​>0, the dominant instability is a fff-wave superfluid for ${p}_{F}{r}_{c}\ensuremath{\lesssim}2$ and a density wave for ${p}_{F}{r}_{c}\ensuremath{\gtrsim}4$. The fff-wave pairing in this repulsive Fermi gas is reminiscent of the conventional Kohn-Luttinger mechanism but has a much higher Tc{T}_{c}Tc​. For attractive bare interactions u0<0{u}_{0}<0u0​<0, the leading instability is ppp-wave pairing. The phase diagram is obtained from a functional renormalization group that treats all competing many-body instabilities in the particle-particle and particle-hole channels on an equal footing.
Abstract We systematically investigate the ground state phase diagram and the finite temperature phase transitions for a Rydberg-dressed Fermi gas loaded in a bilayer optical lattice. When an effective finite-ranged attraction is induced, our self-consistent mean-field calculation shows that the gapped topological (p-wave) superfluids in each layer are coupled together by the s-wave pairing in an intermediate inter-layer distance with a spontaneously modulated phases between these two order parameters. The obtained ground state is a gapless topological superfluid with quantized topological charges characterizing the gapless points, leading to a zero energy flat band at the edges. Finally, we calculate the finite temperature phase diagrams of this two-dimensional gapless superfluid and observe two distinct critical temperatures, demonstrating the fruitful many-body effects on a paired topological superfluids.
The strong interaction between Rydberg atoms can be used to control the strength and character of the interatomic interaction in ultracold gases by weakly dressing the atoms with a Rydberg state. Elaborate theoretical proposals for the realization of various complex phases and applications in quantum simulation exist. Also a simple model has been already developed that describes the basic idea of Rydberg dressing in a two-atom basis. However, an experimental realization has been elusive so far. We present a model describing the ground state of a Bose–Einstein condensate dressed with a Rydberg level based on the Rydberg blockade. This approach provides an intuitive understanding of the transition from pure two-body interaction to a regime of collective interactions. Furthermore it enables us to calculate the deformation of a three-dimensional sample under realistic experimental conditions in mean-field approximation. We compare full three-dimensional numerical calculations of the ground state to an analytic expression obtained within Thomas–Fermi approximation. Finally we discuss limitations and problems arising in an experimental realization of Rydberg dressing based on our experimental results and point out possible solutions for future approaches. Our work enables the reader to straight forwardly estimate the experimental feasibility of Rydberg dressing in realistic three-dimensional atomic samples.
Abstract The interplay between many-body interactions and the kinetic energy gives rise to rich phase diagrams hosting, among others, interaction-induced topological phases. These phases are characterized by both a local order parameter and a global topological invariant, and can exhibit exotic ground states such as self-trapped polarons and interaction-induced edge states. In this work, we investigate a realistic scenario for the quantum simulation of such systems using cold Rydberg-dressed atoms in optical lattices. We consider spinless fermions on a checkerboard lattice, interacting via the tunable-range effective potential induced by the Rydberg dressing. We perform a detailed analysis of the phase diagram at half- and incommensurate fillings, in the mean-field approximation. We furthermore study the stability of the phases with respect to temperature within the mean-field approximation and with respect to quantum fluctuations using the density matrix renormalization group method. Finally, we propose an implementation protocol, and in particular identify attainable regimes of experimental parameters in which the topological properties of the model become accessible. Our work thereby opens a realistic pathway to the outstanding experimental observation of this predicted phase in state-of-the-art cold atom quantum simulators.
We investigate the superfluid transition temperature of quasi-two-dimensional imbalanced Fermi gases beyond the mean-field approximation, through the second-order (or induced) interaction effects. For a balanced Fermi system the transition temperature is suppressed by a factor $\ensuremath{\approx}$2.722.722.72. For imbalanced Fermi systems, the polarization and transition temperature of the tricritical point are significantly reduced as the two-body binding energy $|{\ensuremath{\epsilon}}_{B}|$ increases.
The interplay between many-body interactions and the kinetic energy gives rise to rich phase diagrams hosting, among others, interaction-induced topological phases. These phases are characterized by both a local order parameter and a global topological invariant, and can exhibit exotic ground states such as self-trapped polarons and interaction-induced edge states. In this work, we investigate a realistic scenario for the quantum simulation of such systems using cold Rydberg-dressed atoms in optical lattices. We consider spinless fermions on a checkerboard lattice, interacting via the tunable-range effective potential induced by the Rydberg dressing. We perform a detailed analysis of the phase diagram at half- and incommensurate fillings, in the mean-field approximation. We furthermore study the stability of the phases with respect to temperature within the mean-field approximation and with respect to quantum fluctuations using the density matrix renormalization group method. Finally, we propose an implementation protocol, and in particular identify attainable regimes of experimental parameters in which the topological properties of the model become accessible. Our work, thereby, opens a realistic pathway to the outstanding experimental observation of this predicted phase in state-of-the-art cold atom quantum simulators.